4. Rover on Mars. A robotic rover (initial temperature 300 K maintained by internal heating) was landed on Mars to probe the surface condition. The average surface temperature on Mars is 220 K. During one incident, the rover lost power and started to cool down. Estimate how much time the engineers had to fix the power supply before the rover temperature dropped to a lethal level of 263 K for the onboard electronics. The rover can be approximated as a solid metallic sphere with radius 0.25 m, thermal conductivity 20 W/mK, specific heat 500 J/kg-K, mass density 8103 kg/m and surface emissivity 0.8. Convection from the rover surface can be neglected due to very low air density on Mars. Conduction loss to the ground can also be neglected because of a small contact area. [Hint: What is the mode of heat loss from the rover surface? Estimate the corresponding heat transfer coefficient].